For a mixed graph \(G\) , let \(N^+_{G}(u):=\lbrace v \colon {uv}\in E(G)~{\rm or~} uv\in E(G)\rbrace \)  be the set of out-neighbors of \(u\) , \(N^-_{G}(u):=\lbrace v \colon {vu}\in E(G)~{\rm or~} uv\in E(G)\rbrace \)  be the set of in-neighbors of \(u\) , and \(N_G(u):=N^+_{G}(u)\cup N^-_{G}(u)\)  be the set of
neighbors of \(u\) . The number \(d^+_G(u):=|N^+_{G}(u)|\)  is called the out-degree of \(u\)  in \(G\) , and the number \(d_G(u):=|N^+_{G}(u)|+|N^-_{G}(u)|\)  is called the degree of \(u\)  in \(G\) . The sequence \(d(G):=(d_G(u))_{u\in V(G)}\)  in descending order is called the degree sequence of \(G\) . In the rest of this paper, the order of degree sequences are considered in dictionary order, that is, \((a_1,a_2,\ldots ,a_n)>(b_1,b_2,\ldots ,b_n)\)  if for the minimum \(i\)  with \(a_i\ne b_i\) , we have \(a_i>b_i\) . The (i) of the following lemma in mixed graph is generalized from its undirected graph version [1]}.
